class: center, middle, inverse, title-slide # Lecture 3 ## Summary Statistics ### Psych 10 C ### University of California, Irvine ### 03/30/2022 --- ## Summary Statistics - Another common way in which information from an experiment or a survey can be summarized is by using an statistic. -- - Summary statistics are **functions** of **random variables** in an experiment that can be used to convey information about the location of our observations and how they vary. -- - Not all the variables in an experiment are equally important, so we don't usually look for ways to visualize them, but we still want to make sure that we give all the information we can about our sample. -- - In that case we can use summary statistics to report some of their properties. --- class: inverse, center, middle # Random Variables and Functions --- ## Random variables - Statisticians are very bad at naming objects... -- - So when you think of the words random and variable what comes to mind first? -- - The formal definition is the opposite! -- - Definition: A random variable is a function of the outcomes of an experiment. --- # Functions - Functions have formal definitions, however, what we have to remember is how they "work". -- - Intuitively, we can think of functions as rules about how to associate two groups of "things". -- - For example, if throw a coin and then record if it landed as heads or tails. A function could be a rule that states: - If the outcome is tails then `\(x = 0\)` if the outcome is heads then `\(x = 1\)` -- - This is a simple rule that just let's us assign numbers to a variable `\(x\)` depending on the result of a coin toss. In other words, `\(x\)` is a function of the outcome of the experiment. -- - Another simple function would be `\(y = x + 1\)`. - This function, tells us that whatever the value of `\(x\)` is, we can get the value of `\(y\)` by adding `\(1\)` to `\(x\)`. -- - Regardless of how complex they loo,k we can think of functions as a "rode-map" that specifies how we get from the values of one variable to the values of another. --- ## Back to Random Variables - Random variables are neither random nor variables, they are simply the rules we use to assign numbers to the outcomes of an experiment. -- - In other words they are deterministic functions (see statisticians are really bad at naming).